We know that momentum is conserved in an inelastic collision, which means the
total momentum of the entire system will be the same before and after the
crash. If we find the sum of the momenta of the car (
) and the truck
(
) before the crash,
we will have the momentum of the resulting ``mergemobile'' (
) afterwards.


Since the two vectors are perpendicular (north & east) we can use Pythagorus' equation to find the total momentum of the system, and therefore the momentum of the smashed mess.

Now to find the velocity of the whole mess

Of course, you need to know the angle:
